1,577 research outputs found
Nonpointlike Particles in Harmonic Oscillators
Quantum mechanics ordinarily describes particles as being pointlike, in the
sense that the uncertainty can, in principle, be made arbitrarily
small. It has been shown that suitable correction terms to the canonical
commutation relations induce a finite lower bound to spatial localisation.
Here, we perturbatively calculate the corrections to the energy levels of an in
this sense nonpointlike particle in isotropic harmonic oscillators. Apart from
a special case the degeneracy of the energy levels is removed.Comment: LaTeX, 9 pages, 1 figure included via epsf optio
Quantum gravity effects on statistics and compact star configurations
The thermodynamics of classical and quantum ideal gases based on the
Generalized uncertainty principle (GUP) are investigated. At low temperatures,
we calculate corrections to the energy and entropy. The equations of state
receive small modifications. We study a system comprised of a zero temperature
ultra-relativistic Fermi gas. It turns out that at low Fermi energy
, the degenerate pressure and energy are lifted. The
Chandrasekhar limit receives a small positive correction. We discuss the
applications on configurations of compact stars. As increases,
the radius, total number of fermions and mass first reach their nonvanishing
minima and then diverge. Beyond a critical Fermi energy, the radius of a
compact star becomes smaller than the Schwarzschild one. The stability of the
configurations is also addressed. We find that beyond another critical value of
the Fermi energy, the configurations are stable. At large radius, the increment
of the degenerate pressure is accelerated at a rate proportional to the radius.Comment: V2. discussions on the stability of star configurations added, 17
pages, 2 figures, typos corrected, version to appear in JHE
Torus invariant divisors
Using the language of polyhedral divisors and divisorial fans we describe
invariant divisors on normal varieties X which admit an effective codimension
one torus action. In this picture X is given by a divisorial fan on a smooth
projective curve Y. Cartier divisors on X can be described by piecewise affine
functions h on the divisorial fan S whereas Weil divisors correspond to certain
zero and one dimensional faces of it. Furthermore we provide descriptions of
the divisor class group and the canonical divisor. Global sections of line
bundles O(D_h) will be determined by a subset of a weight polytope associated
to h, and global sections of specific line bundles on the underlying curve Y.Comment: 16 pages; 5 pictures; small changes in the layout, further typos
remove
Synthèse, structure et activités biologiques des complexes de nickel (II), zinc (II) et cadmium (II) du 3-thiophène aldéhyde (3TTSCH) de la thiosemicarbazone
Affine T-varieties of complexity one and locally nilpotent derivations
Let X=spec A be a normal affine variety over an algebraically closed field k
of characteristic 0 endowed with an effective action of a torus T of dimension
n. Let also D be a homogeneous locally nilpotent derivation on the normal
affine Z^n-graded domain A, so that D generates a k_+-action on X that is
normalized by the T-action. We provide a complete classification of pairs (X,D)
in two cases: for toric varieties (n=\dim X) and in the case where n=\dim X-1.
This generalizes previously known results for surfaces due to Flenner and
Zaidenberg. As an application we compute the homogeneous Makar-Limanov
invariant of such varieties. In particular we exhibit a family of non-rational
varieties with trivial Makar-Limanov invariant.Comment: 31 pages. Minor changes in the structure. Fixed some typo
On the geometry of quantum constrained systems
The use of geometric methods has proved useful in the hamiltonian description
of classical constrained systems. In this note we provide the first steps
toward the description of the geometry of quantum constrained systems. We make
use of the geometric formulation of quantum theory in which unitary
transformations (including time evolution) can be seen, just as in the
classical case, as finite canonical transformations on the quantum state space.
We compare from this perspective the classical and quantum formalisms and argue
that there is an important difference between them, that suggests that the
condition on observables to become physical is through the double commutator
with the square of the constraint operator. This provides a bridge between the
standard Dirac procedure --through its geometric implementation-- and the
Master Constraint program.Comment: 14 pages, no figures. Discussion expanded. Version published in CQ
Generalized Uncertainty Principle, Modified Dispersion Relations and Early Universe Thermodynamics
In this paper, we study the effects of Generalized Uncertainty Principle(GUP)
and Modified Dispersion Relations(MDRs) on the thermodynamics of
ultra-relativistic particles in early universe. We show that limitations
imposed by GUP and particle horizon on the measurement processes, lead to
certain modifications of early universe thermodynamics.Comment: 21 Pages, 3 eps Figure, Revised Versio
Stability conditions and positivity of invariants of fibrations
We study three methods that prove the positivity of a natural numerical
invariant associated to parameter families of polarized varieties. All
these methods involve different stability conditions. In dimension 2 we prove
that there is a natural connection between them, related to a yet another
stability condition, the linear stability. Finally we make some speculations
and prove new results in higher dimension.Comment: Final version, to appear in the Springer volume dedicated to Klaus
Hulek on the occasion of his 60-th birthda
- …